The ending to Max Payne 2 teases with a message at the end of the credits proclaiming, "Max Payne's journey into the night will continue", but the story itself seems to be over, Max has found peace with his life of guilt and out of both games, Max is the only character left alive (apart from the Dead on Arrival ending on Max Payne 2 where Mona lives). The third game in the series was announced by Jeffrey L. Lapin, the CEO of Take-Two Interactive in 2004. There have been no further announcements regarding the matter – not even a developer for the third game has been named. Remedy Entertainment's name was mentioned in the announcement. At the same time, a post on Shacknews, apparently from someone claiming to be Mikael Kasurinen, a level designer for Max Payne 2, read "FYI: We are not making Max Payne 3.", though this has not been confirmed by anyone from Take Two. GameSpot notes status of the game is cancelled.

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Keep your eyes in the clouds, your feet on the ground, and dance to the drums of your own song.

Its likely not going to happen anytime soon (like in the next couple of years) but it's anyones guess after that...right now Sam Lake (creator/writer of Max Payne series) is busy working on the 'Alan Wake' game project. Once it's done he may start writing and begin work on the 3rd, but again, its anyone's guess whether a Max Payne 3 will ever come out...

My guess is we will see another game, but not for a long, long time... On another note you'll be interested to know that they've picked up the plans for a Max Payne feature film.